I need to find the largest and smallest value for f(x,y) in a particular domain.
and
I found the stationary points but I have trouble when I insert the domain in f(x,y) as the answer I get is not right.
How would you solve the problem?
Thanks
I need to find the largest and smallest value for f(x,y) in a particular domain.
and
I found the stationary points but I have trouble when I insert the domain in f(x,y) as the answer I get is not right.
How would you solve the problem?
Thanks
Hello, sebasto!
The domain gave me headaches, so I ignored it at the beginning.
Equate the partial derivative to zero and solve.Find the maximum and minimum for in a given domain.
. .
. .
From [2], we have: .
If , [1] becomes: .
. . We have two critical points: .
If , [1] becomes: .
. . We have one more critical point: .
Second Partial Test: .
At . . . saddle points
At . . . extremum
. . . . . positive, concave up
Therefore: . . . . which is in the domain.
Edit: We must find the maximum(s) along the circumference of that circle.
I would use Lagrange multipliers: .
I got the same saddle points and minimum with their respective function value, but the answer is
smallest value
Largest value
Maybe I formulated the question wrong, I'm looking for the smallest and largest value in the range